Lie minimal Weingarten surfaces
Differential Geometry
2023-10-25 v1
Abstract
We consider Lie minimal surfaces, the critical points of the simplest Lie sphere invariant energy, in Riemannian space forms. These surfaces can be characterized via their Euler-Lagrange equations, which take the form of differential equations of the principal curvatures. Surfaces with constant mean curvature that satisfy these equations turn out to be rotational in their space form. We generalize in flat ambient space: here surfaces where the principal curvatures satisfy an affine relationship as well as elliptic linear Weingarten surfaces are rotational as well.
Cite
@article{arxiv.2310.15695,
title = {Lie minimal Weingarten surfaces},
author = {Joseph Cho and Masaya Hara and Denis Polly and Tomohiro Tada},
journal= {arXiv preprint arXiv:2310.15695},
year = {2023}
}
Comments
11 pages